diff --git a/src/storage/src/source/persist_source.rs b/src/storage/src/source/persist_source.rs
index d20617d5e96bf..b5b84a5cca6e5 100644
--- a/src/storage/src/source/persist_source.rs
+++ b/src/storage/src/source/persist_source.rs
@@ -266,9 +266,6 @@ where
     let (mut update_output, update_output_stream) = fetcher_builder.new_output();
     let (mut consumed_part_output, consumed_part_output_stream) = fetcher_builder.new_output();
 
-    let update_output_port = update_output_stream.name().port;
-    let consumed_part_port = consumed_part_output_stream.name().port;
-
     // Re-used state for processing and building rows.
     let mut datum_vec = mz_repr::DatumVec::new();
     let mut row_builder = Row::default();
@@ -305,12 +302,8 @@ where
                     // panicking, so swap them to an owned version.
                     data.swap(&mut buffer);
 
-                    let update_cap = cap.delayed_for_output(cap.time(), update_output_port);
-                    let mut update_session = output_handle.session(&update_cap);
-
-                    let consumed_part_cap = cap.delayed_for_output(cap.time(), consumed_part_port);
-                    let mut consumed_part_session =
-                        consumed_part_output_handle.session(&consumed_part_cap);
+                    let mut update_session = output_handle.session(&cap);
+                    let mut consumed_part_session = consumed_part_output_handle.session(&cap);
 
                     for (_idx, part) in buffer.drain(..) {
                         let (consumed_part, fetched_part) =